FORD F-350 ALTERNATOR PROBLEM

2003 Ford F-350

2003 - Ford F350, 6.0L Diesel, Lariat, Dully, Fully Loaded:
Battery light goes on and off randomly during all types of driving and temperatures.
Cannot find any loose wires anywhere.
Just replaced both batteries and problem still there. The alternator test good - (~14.6V when running).
Batteries charge right up to ~14.2V from cold start in under 2 minutes.
Mechanic now says to replace the alternator! What?
What does this battery light monitor anyway?
Is there some kind of sensor that could be bad, making the idiot light go on and off?
Should I be concerned about this problem?
Hate to spend hundreds of dollars for an alternator when the problem is only a stupid sensor somewhere.
Help please.
BJay